14 research outputs found

    Zero and Low Energy Thresholds in Quantum Simulation

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    Quantum simulation is the process of simulating a quantum mechanical system using either a quantum or a classical computer. Because quantum mechanical systems contain a large number of entangled particles, they are hard to simulate on a classical computer. It is the task of computational complexity theorists to estimate the amount of resources to do the same number of operations on either classical or quantum devices. This report first summarizes the state of the art in the field of quantum computing, and gives an example of a model of quantum computer and examples of quantum algorithms that are currently being researched. Then our own research about k-local quantum Hamiltonians is discussed. We developed programs to determine if a particular kind of k-local Hamiltonian has zero-energy solutions. First, to familiarize ourselves with quantum algorithms, we implemented a recently discovered polynomial-time 2-QSAT algorithm called SolveQ. Then we wrote several versions of brute force 7-variable 3-QSAT solvers and conducted experiments for the threshold of satisfiability. We empirically determined that the thresholds for the four versions, Versions 3, 4, 5, and 6, are 0.741, 1.714, 1.714, and 0.571, respectively. In addition, experiments were conducted involving the 6-qubit Ising model, working on which caused us to realize how inefficient the classical computer really is at simulating quantum mechanical systems. Our conclusion is that quantum simulation is much less feasible than classical simulation on a classical computer

    Combining Cubic Dynamical Solvers with Make/Break Heuristics to Solve SAT

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    Dynamical solvers for combinatorial optimization are usually based on 2superscript{nd} degree polynomial interactions, such as the Ising model. These exhibit high success for problems that map naturally to their formulation. However, SAT requires higher degree of interactions. As such, these quadratic dynamical solvers (QDS) have shown poor solution quality due to excessive auxiliary variables and the resulting increase in search-space complexity. Thus recently, a series of cubic dynamical solver (CDS) models have been proposed for SAT and other problems. We show that such problem-agnostic CDS models still perform poorly on moderate to large problems, thus motivating the need to utilize SAT-specific heuristics. With this insight, our contributions can be summarized into three points. First, we demonstrate that existing make-only heuristics perform poorly on scale-free, industrial-like problems when integrated into CDS. This motivates us to utilize break counts as well. Second, we derive a relationship between make/break and the CDS formulation to efficiently recover break counts. Finally, we utilize this relationship to propose a new make/break heuristic and combine it with a state-of-the-art CDS which is projected to solve SAT problems several orders of magnitude faster than existing software solvers

    Quantum algorithms

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    Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 1999.Includes bibliographical references (leaves 89-94).by Daniel S. Abrams.Ph.D

    Quantum computation beyond the circuit model

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2008.Includes bibliographical references (p. 133-144).The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other models of quantum computation exist which provide useful alternative frameworks for both discovering new quantum algorithms and devising new physical implementations of quantum computers. In this thesis, I first present necessary background material for a general physics audience and discuss existing models of quantum computation. Then, I present three new results relating to various models of quantum computation: a scheme for improving the intrinsic fault tolerance of adiabatic quantum computers using quantum error detecting codes, a proof that a certain problem of estimating Jones polynomials is complete for the one clean qubit complexity class, and a generalization of perturbative gadgets which allows k-body interactions to be directly simulated using 2-body interactions. Lastly, I discuss general principles regarding quantum computation that I learned in the course of my research, and using these principles I propose directions for future research.by Stephen Paul Jordan.Ph.D
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